Structure and suffering

Question 1

Born Oppenheimer Approximation

Answer 1

The electronic and nuclear motions are uncoupled and can be separated out.

Why? Atomic nucleus is heavier than electrons by 1000 times.

Question 2

Terms in the Hamiltonian

Answer 2

Question 3

Pauli principle

Answer 3

The total wavefunction (including spatial and spin components) must be antisymmetric with respect to the interchange of any two fermions (electorns) and symmetric with respect to the interchange of any two bosons (integer spin).

Question 4

Wavefunctions, Ψ - what they contain and how are they found.

Answer 4

Wave functions, Ψ, contain all the information on the quantum system – found via
Schrödinger equation.

Question 5

Probability of finding the particle in a small volume d𝜏

Answer 5

If the wave function has the value, 𝜓, at point 𝒓, the probability if finding the particle in
the small volume d𝜏 around 𝒓 is 𝜓^2d𝜏.

Question 6

What does every observable quantity correspond to?

Answer 6

Every observable physical quantity (e.g. energy, 𝐸) corresponds to linear, Hermitian
operator (e.g. Hamiltonian ෡
𝐻)

Question 7

Is Ψ𝑛𝑒𝑤 = 𝑐1Ψ 1 + 𝑐2Ψ2 an eigenfunction?

Answer 7

If the wave functions Ψ 1 and Ψ2 both represent eigenfunctions of the system, then any
liner combination, Ψ𝑛𝑒𝑤 = 𝑐1Ψ 1 + 𝑐2Ψ2, is also an eigenfunction.

Question 8

Eigenvectors of a Hermitian operator - orthogonal or no.

Answer 8

The eigenvectors of a Hermitian operator are orthogonal, so Ψ𝑚
∗ Ψ𝑛 = 0 when 𝑛 ≠ m

Question 9

What does physical measurements of observables correspond to?

Answer 9

Physical measurements of observables give values that correspond to a weighted sum of the eigenvalues of the observable.

Question 10

Secular equations

Answer 10

Question 11

Secular matrix

Answer 11

Question 12

Secular determinant

Answer 12

Question 13

Huckel theory assumptions

Answer 13

Question 14

Huckel theory approximations

Answer 14

Question 15

Aromatic molecules

Answer 15

Aromatic molecules have an additional stability owing to the HOMO being fully filled
with spin paired electrons.

n = 4k+2

Question 16

Antiaromatic molecules

Answer 16

Antiaromatic molecules are highly unstable and reactive when in the cyclic planar form

Question 17

Non aromatic molecules

Answer 17

All other molecules that do not match the above rules are nonaromatic.